5. Men's faces have higher width-to-height ratios than women's, on average. This turns out to reflect a difference in te

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5. Men's faces have higher width-to-height ratios than women's, on average. This turns out to reflect a difference in testosterone expression during puberty. Testosterone is also known to predict aggressive behavior. Does face shape predict aggression? To test this, Carre and McCormick (2008) compared the face width-to-height ratios of 21 university hockey players with the average number of penalty minutes awarded per game for aggressive infractions like fighting or cross-checking. The results from were analyzed in SAS, with output given on page 8. (A - 6 pts.) At a significance level of 0.05, does the output indicate that there is a linear relationship between width-to-height ratio and penalty minutes? State the appropriate null and alternative hypotheses. Report a p-value, and explain how you used it to make your decision. (B - 6 pts.) State and interpret the slope of the best-fit line. What does it tell you about the relationship between face width-to-height ratio and average number of aggressive infraction penalty minutes? Include appropriate units. (C-10 pts.) Report the equation of the best-fit-line relating X = face width-to-height ratio and Y = average penalty minutes for aggressive infractions. Use this equation to predict the average number of aggressive infraction penalty minutes for a male university hockey player with a face width-to- height ratio of 2.

Page 8 of 8 SAS OUTPUT FOR #5 The REG Procedure Model: MODELI Dependent Variable: minutes Number of Observations Read 21 Number of Observations Used 21 Analysis of Variance Sum of Mean Source DF Squares Square FValue Pr>F Model 2 80049 2.89040 7.60 0.0121 Error 19 7.13837 037570 Corrected Total 2010.02807 1 Root MSE 061295 R-Square 02882 Dependent Mean 127667 Ad R-Sq 0.2506 Coeff Var 4801150 DF Variable Intercept face_ratio Parameter Estimates Parameter Standard Estimate Error Value Pr>1 450450 2.08855 216 0.0140 3.18898 1.14971 277 00121 1 Fe Portes 20 fre Cor

5. Men's faces have higher width-to-height ratios than women's, on average. This turns out to reflect a difference in testosterone expression during puberty. Testosterone is also known to predict aggressive behavior. Does face shape predict aggression? To test this, Carre and McCormick (2008) compared the face width-to-height ratios of 21 university hockey players with the average number of penalty minutes awarded per game for aggressive infractions like fighting or cross-checking. The results from were analyzed in SAS, with output given on page 8. (A-6 pts.) At a significance level of 0.05, does the output indicate that there is a linear relationship between width-to-height ratio and penalty minutes? State the appropriate null and alternative hypotheses. Report a p-value, and explain how you used it to make your decision. ( - 6 pts.) State and interpret the slope of the best-fit line. What does it tell you about the relationship between face width-to-height ratio and average number of aggressive infraction penalty minutes? Include appropriate units. (C-10 pts.) Report the equation of the best-fit-line relating X-face width-to-height ratio and Y - average penalty minutes for aggressive infractions. Use this equation to predict the average number of aggressive infraction penalty minutes for a male university hockey player with a face width-to- height ratio of 2